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Chapter 2: Problem 19

Solve each equation, and check your solution. $$ 2=p+15 $$

Short Answer

Expert verified
The solution is p = -13.

Step by step solution

01

Isolate the variable

Start by isolating the variable (p) on one side of the equation. To do this, subtract 15 from both sides: `2 - 15 = p + 15 - 15` `-13 = p`
02

Verify the solution

To verify the solution, substitute dumdumdumdumdum `p`umdumdumdumdumdum with dum ` p` umdumdum ` = -13` umdum ` back` into the original equation: `2 == ` `-13 + `15` ` 2 == 2 `. Since both sides of the equation are equal, `the solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Variable
To solve an equation like \(2 = p + 15\), you need to isolate the variable. This process helps you find the value of the unknown (in this case, \(p\)). The key step involves performing the same mathematical operation on both sides of the equation. Here, we want to get \(p\) by itself on one side. So, we subtract 15 from both sides of the equation to cancel out the 15 on the right side. This gives us:
\(-13 = p\).
Now, \(p\) is isolated, and we have our solution!
Verifying Solutions
Once you've isolated the variable and found a solution, it鈥檚 important to verify that the solution is correct. To do this, substitute the value you found back into the original equation. In our example, we substitute \(p = -13\) back into the equation \(2 = p + 15\):
\(2 = -13 + 15\)
Simplifying the right side, we end up with \(2 = 2\).
Since both sides of the equation are equal, our solution is verified as correct. Verification helps you confidently know your answer is accurate.
Basic Algebra
Basic algebra involves understanding and manipulating mathematical symbols and numbers to solve equations. There are several key concepts to know:
  • Variables: Symbols like \(p\) that represent unknown values.
  • Operations: The basic operations (addition, subtraction, multiplication, and division) used to manipulate quantities.
  • Equations: Mathematical statements that show two expressions are equal, often involving variables.

Solving linear equations, like \(2 = p + 15\), requires applying these basic algebraic skills to isolate the variable and find its value. By practicing these steps, you can develop a strong understanding of how to solve similar problems in algebra.

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Most popular questions from this chapter

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